Practical Linear Algebra: A Geometry Toolbox, Third edition
Gerald Farin & Dianne Hansford
CRC Press, Taylor & Francis Group, An A K Peters Book, 2013

Vector field visualization
Some example of vector field visualization using Mathematica.

Several sample functions are given or choose your own.

(* ------- Function selection ------- *)
(* More example functions:
{x,-y}  {-y,x}  {x^2,0} 
*)
myfct[x_,y_]:= {x,-y};
d1= {-3,3};
d2 = {-3,3};

VectorPlot[myfct[x,y],{x,d1[[1]],d1[[2]]},{y,d2[[1]],d2[[2]]}]

VectorPlot[myfct[x,y],{x,d1[[1]],d1[[2]]},{y,d2[[1]],d2[[2]]},VectorStyle->{Black,"Disk"}]
VectorDensityPlot[myfct[x,y],{x,d1[[1]],d1[[2]]},{y,d2[[1]],d2[[2]]}]
StreamDensityPlot[myfct[x,y],{x,d1[[1]],d1[[2]]},{y,d2[[1]],d2[[2]]},ColorFunction->"ThermometerColors"]